63.7.3 problem 1(c)

Internal problem ID [13043]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.2.3 Complex eigenvalues. Exercises page 94
Problem number : 1(c)
Date solved : Wednesday, March 05, 2025 at 08:59:13 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+9 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 8

ode:=diff(diff(x(t),t),t)+9*x(t) = 0; 
ic:=x(0) = 1, D(x)(0) = 0; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x \left (t \right ) = \cos \left (3 t \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 9

ode=D[x[t],{t,2}]+9*x[t]==0; 
ic={x[0]==1,Derivative[1][x][0 ]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \cos (3 t) \]

✓ Sympy. Time used: 0.073 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(9*x(t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 1, Subs(Derivative(x(t), t), t, 0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \cos {\left (3 t \right )} \]